Yes, it could. Most people with high blood pressure are advised not to take these kinds of drugs because it can cause a rise in pressure when you take it so therefore when you stop taking, blood pressure drops again (even without high blood pressure).
If the the active ingredient in Unisom is diphenhydramine (benedryl) this is an anti-histamine and doesn't effect blood pressure. It is,however, very well known for it's side effect of making you sleepy. People with allergies are often given decongestants along with the anti-histamine and decongestants are vaso-dilators which do definitely drop your blood pressure. All of your blood vessels open up so the pressure goes down. I have had allergies all my life and I also am a retired research scientist who worked in cellular and molecular immunology. So that's all that I know.
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